Patients are being asked to enter this research study to investigate the safety and efficacy of Enoxaparin 1 X daily or 2 X daily compared with continuous infusion heparin in the treatment of blood clots in the legs and/or lungs. Blood clots in the legs are estimated to occur in 48 of 100,000 patients per year and lung clots are estimated in 23 of 100,000 per year. Currently, most doctors treat these clots with blood thinners such as heparin given intravenously and warfarin, given orally. Left untreated, leg clots reoccur in 31.4 to 51.7% of patients and fatal lung clots occur in 8.0 to 26.2% of patients who have leg clots which are treated only with bed rest. Enoxaparin is a type of heparin product that is approved for use in humans in many countries. In animals, it has been shown to cause less bleeding than heparin at the same doses. In recent studies, it has been shown that heparin type products similar to enoxaparin are effective in the treatment of leg clots also, in a recent study of patients with leg and/or lung clots, it was determined that enoxaparin might be effective and well tolerated for treatment of these clots. Researchers are looking for better anticoagulants with less bleeding and other side effects because warfarin and heparin have serious side effects and frequent bleeding episodes.